Dispersion curves for lamb waves using analytical solutions and the scaled-boundary finite element method

This article deals with the estimation of dispersion curves and wave structures for Lamb waves performed using the analytical scheme and Scaled Boundary Finite Element Method (SBFEM). In the SBFEM approach, the cross-sections of the waveguide are discretized by isoparametric elements. This formulation leads to an eigenvalue problem for the calculation of wavenumber-frequency couples, which can be efficiently solved. These results are compared with those analytical solutions obtained from the characteristic equations of Rayleigh-Lamb whose solutions describe the symmetric and antisymmetric modes for isotropic and constant cross-section plates. Both approaches are implemented in the Matlab environment. The results demonstrate that both approaches are effective in calculating the dispersion curves and wave structure, but for the SBFEM approach, an optimized number of isoparametric quadratic elements yield a comparable time with the analytical calculation. However, as the thickness increase, the computational effort also increases.